What is the value of the first

Question

The sum is 231. The first is 20 more than the second. The sum of the first two is 6 more than twice third

Answer 1

These can be confusing, so lets call each number by a letter.

The first number will be A.

The second number will be B.

The third number will be C.

Anytime you see the word "is", in math that is an EQUAL sign (=)

Now we just translate each sentence into math.

"The sum is 231" becomes A + B + C = 231

"The first is 20 more than the second" becomes A = 20 + B

"The sum of the first two is 6 more than twice third" becomes

A + B = 6 + 2C

Notice in the first equation we have A + B + C = 231, and if we group it as (A + B) + C = 231, our last equation has (A + B). So we can replace the "A + B" in the first equation with "6 + 2C".

6 + 2C + C = 231

6 + 3C = 231

3C = 225

C = 225/3 = 75

So go back and find the others, knowing that C = 75

A + B = 6 + 2(75)

A + B = 156

And we know that A = 20 + B

20 + B + B = 156

2B = 136

B = 68

Using both B=68 and C=75, plug into A + B + C = 231 to find A

A + 68 + 75 = 231

A + 143 = 231

A = 88

It looks like A = 88, B = 68, C = 75

Let's check:

A + B + C = 88 + 68 + 75 = 231√

Is A 20 more than B? Well B is 68, 20 more would be 88, and A=88√

Is A + B = 6 + 2C? A + B = 156 6 + 2C = 156√

So our answers are correct:

A=88

B=68

C=75